OBJ files and vertex colours
The .obj format specification doesn't contain any description of vertex color attributes. Some software like MeshLab or Agisoft Metashape extend the .obj format and include the vertex colors after the coordinates.

v 3.112696 -9.640543 15.350909 0.592157 0.517647 0.537255


Since it is not covered by the specification, Blender provides no ability to import vertex colors. There are other formats that do allow to store vertex color which can be imported into Blender, for example .ply.